A punctured torus $Sigma(1,1)$ is a building block of oriented surfaces. The goal of this paper is to formulate the matrix presentations of elements of the Teichmuller space of a punctured torus. Let $cal{C}$ be a matrix presentation of the boundary component of $Sigma(1,1)$.In the level of the matrix group $mathbb{SL}$($mathbb2,R$) we shall show that the trace of $cal{C}$ is always negative.